Answer to Question #260763 in Calculus for jia

Question

y = x (x-3)⁴

Answer 1

Solution;

$Given;$

$y=x(x-3)^4$

$\frac{d}{dx}[(x-3)^4x]$

Applying the product rule;

$\frac{d}{dx}[(x-3)^4].x+(x-3)^4\frac{d}{dx}[x]$

We have;

$4(x-3)^3[\frac{d}{dx}(x-3)].x+(x-3)^4.1$

Differentiate the remaining part as;

$4(x-3)^3[1-0].x+(x-3)^4$

Rewrite as;

$y'=(5x-3)(x-3)^3$